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Sum of Odd Natural Numbers Experiment Class 10 Maths Practical NCERT

The experiment to determine Sum of Odd Natural Numbers are part of the Class 10 Maths Lab Manual provides practical activities and experiments to help students understand mathematical concepts effectively. It encourages interactive learning by linking theoretical knowledge to real-life applications, making mathematics enjoyable and meaningful.

Maths Lab Manual Class 10 CBSE Sum of Odd Natural Numbers Experiment

Determine Sum of Odd Natural Numbers Class 10 Practical

Objective
To verify that the sum of first n odd natural numbers, 1 +3 + 5+ … + (2n— 1) = n by paper activity.

Prerequisite Knowledge

  1.  Natural numbers (i.e. counting numbers  e.g., 1, 2, 3, 4, …)
  2.  Odd natural numbers (Natural numbers which are not divisible by 2  i.e.  1, 3, 5, …)
  3.  Even natural numbers (Natural numbers which are divisible by 2  i.e.  2, 4, 6,…)
  4. Formula to find the n ‘ term of an AP i.e.,
    an = a+ (n—1) d
    where a—> first term,    d—> common difference,   n —> no. of terms
  5.  For odd natural numbers 1,3,5,…, term is
    an =1 + (n— 1). 2 = (2n— 1)
  6.  Area of squares.

Materials Required
Squared papers, sketch pens, pencil, a pair of scissors, geometry box, fevicol, white drawing sheets

Procedure

    1.  Take a squared chart paper of size n units X n units (Take n— 9).
      NCERT Class 10 Maths Lab Manual - Sum of Odd Natural Numbers 1
    2.  Paste it on a white sheet.
    3. Colour the internal squares with different 9 colours as shown in the fig. (i).

NCERT Class 10 Maths Lab Manual - Sum of Odd Natural Numbers 2
4. Put a black dot on each of the internal coloured squares as shown in fig.(ii)

NCERT Class 10 Maths Lab Manual - Sum of Odd Natural Numbers 3

Observation
NCERT Class 10 Maths Lab Manual - Sum of Odd Natural Numbers 4

Result
The sum of first n odd natural numbers is n i.e., 1 + 3 + 5 + 7 + … + (2» —1) = n

Learning Outcome
Through this activity students are able to find that the sum of first n odd natural numbers n2  i.e., \(\sum { (2n-1) }\) =n2

Activity Time

  1.  Find out the sum of first fifteen odd natural numbers with the help of above activity and verify the result using the formula \(\sum { (2n-1) }\) = n2
  2. Find the sum of (11 + 13 + …+21) using the result of this activity.

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Viva Voce

Question 1:
What is the sum of first n natural numbers ?
Answer:
Sn = \(\frac { n(n+1) }{ 2 }\)

Question 2:
Give the formula for sum of first (« + 1) natural numbers.
Answer:
Sn+1 =\(\frac { (n+2)(n+1) }{ 2 }\)

Question 3:
What is the sum of first n multiples of 5 ?
Answer:
\(\frac { 5\times n(n+1) }{ 2 } \)

Question 4:
Whatisthesumof 2 + 6 + 10 + 14 + 18 + … + 10 terms ?
Answer:
200
[Hint: 2 [1 + 3 + 5 +… + 10 terms] =2 x 102= 200]

Question 5:
What is the #th term of  1 + 3 + 5 ?
Answer:
an =(2n— 1)

Question 6:
What is the n th term of 2 + 4 + 6 ?
Answer:
an = 2n

Question 7:
Give the formula for the sum to n terms of an AP.
Answer:
Sn= \(\frac { n }{ 2 } [2a+(n-a)d]\)

Question 8:
Define odd numbers and which is the first odd natural number.
Answer:
Numbers which are not divisible by 2 are known as odd numbers. 1 is the first odd natural number.

Multiple Choice Questions

Question 1:
Find n for  \(\frac { n(n+1) }{ 2 }\) =55
(a)  -11
(b)  10
(c)   11
(d) None of these

Question 2:
Using, \(\frac { n(n+1) }{ 2 }\) evaluate 1 + 3 + 5 + 7 + 9.
(a) 24
(b) 23
(c) 25
(d) 26

Question 3:
If  n th term of an AP is (2n + 1), find the sum of first n terms of the AP.
(a) n(n+ 2)
(b) n(n -2)
(c) (n2—2)
(d) None of these

Question 4:
For AP 5 + 4 + 3 + 2 + 1+ 0 + (-1) + what should be its last term so that sum of all terms is zero ?
(a)  -4
(b)  -7
(c)  -5
(d)  None of these

Question 5:
In AP 16 + 12 + 8 + 4 + 0 + (-4) + (-8) + (-12) +S7 is
(a)  28
(b)  16
(c)  20
(d)  None of these

Question 6:
Common difference of an  AP \(sqrt { 2 } ,\sqrt { 8 } ,\sqrt { 18 } ,\sqrt { 32 } \)   is
(a) \(\sqrt { 3 } \)
(b) \(\sqrt { 2 } \)
(c) 2\(\sqrt { 3 } \)
(d) 4

Question 7:
First term of an AP is p and its common difference is q then its 10th term is
(a) 9p + q
(b) p-9q
(c) p + 9q
(d) None of these

Question 8:
The sum of first npositive integer Sn is
(a)  \(\frac { n(n-1) }{ 2 } \)
(b)  \(\frac { n(n+1) }{ 2 } \)
(c)  \(\frac { n }{ 2 } [2a+(n-1)d]\)
(d)  a+(n-1)d

Question 9:
20th term of the series 4, 7, 10, ……. is
(a) 61
(b) 60
(c) 59
(d) None of these

Question 10:
Choose the correct option : First four terms of the AP whose first term is —1 and common difference is \(\frac { 1 }{ 2 } \)
(a)  -1 , –\(\frac { 1 }{ 2 } \) , \(\frac { 1 }{ 2 } \) , 0
(b)  -1 , 0 ,-\(\frac { 1 }{ 2 } \) , \(\frac { 1 }{ 2 } \)
(c)  -1 , –\(\frac { 1 }{ 2 } \) , 0,  \(\frac { 1 }{ 2 } \)
(d)  0 , –\(\frac { 1 }{ 2 } \) ,  \(\frac { 1 }{ 2 } \) , 1

Answers
1.  (b)
2.  (c)
3.  (a)
4.  (c)
5.  (a)
6.  (b)
7.  (c)
8.  (b)
9.  (a)
10.(c)

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NCERT Class 10 Maths Lab Manual